Since the two particles a traveling at the same speed v, relative to each other they are stationary. This means that as measured from a reference frame fixed to any of the particles, the distance between them l0 will be the original distance. The distance measured by someone in the Laboratory will however be a shrunk version of the original distance between the particles given by 
. Similarly, time will appear to be slower in the reference frame fixed to the particles compared to the time measured in the Laboratory. So while the time interval between collisions measured in the Laboratory reference frame is 
, the same however, when measured in the reference frame fixed to the particles will be a lesser (since time is slower) given by 
.Solution to the Problem in Reference Frame of the Particles:
In the reference frame of the particles we have,
Solution to the Problem in the Laboratory Reference Frame :
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